In this talk we introduce a smoothing Newton method for solving the weakly nonlinear complementarity problem, by equivalently transforming a class of weakly nonlinear complementarity problems into a modulus equation, and introducing a smoothing approximation of the absolute value function. Under some mild assumptions, we prove that the proposed method has global convergence and locally quadratical convergenc ratee. Especially, the global convergence results do not need a priori existence of an accumulation point with some suitable conditions.